Problem: A circle has a circumference of ${10}$. It has an arc of length $\dfrac{9}{2}$. What is the central angle of the arc, in degrees?
Solution: The ratio between the arc's central angle $\theta$ and $360^\circ$ is equal to the ratio between the arc length $s$ and the circle's circumference $c$. $\dfrac{{\theta}}{360^\circ} = \dfrac{{s}}{{c}}$ $\dfrac{{\theta}}{360^\circ} = {\dfrac{9}{2}} \div {10}$ $\dfrac{{\theta}}{360^\circ} = \dfrac{9}{20}$ ${\theta} = \dfrac{9}{20} \times 360^\circ$ ${\theta} = 162^\circ$ ${10}$ ${\dfrac{9}{2}}$ ${162^\circ}$